PRP Records

Probable Primes Top 10000

(177649 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
90015^73096-1700651092Enzo Doria02/2013
900210^51091-70151091Robert Price06/2017
9003(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
90042^169706-27055151087Gary Barnes08/2009
9005(2^169696+5)/2151083Lelio R Paula01/2012
9007(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
900611^49051-876051082Enzo Doria02/2013
9008(24737*2^169672+1)/2751080Lelio R Paula05/2014
90092^169677+1609551078Lelio R Paula05/2009
90102^169659-13551073Lelio R Paula01/2011
90112^169638-11318351067Enzo Doria07/2014
9012(29*2^169622-1)/234653118551054Lelio R Paula01/2014
9013(10^51054+17)/951054Robert Price10/2014
9014(24737*2^169577+1)/551052Lelio R Paula05/2014
901511^49021-7851051Lelio R Paula01/2013
901618^40669+6151051Lelio R Paula01/2013
901714038^4327+4327^1403851045Hans Havermann02/2016
90182^169555-15951042Lelio R Paula01/2011
901991^26054-251041Lelio R Paula08/2013
9020Phi(101775,10)/162840151034Makoto Kamada05/2015
902197*10^51027-351029Robert Price01/2017
90222^169499-264751025Yves Minet07/2014
90235*6^65567+751022Lelio R Paula09/2014
902414763^2858+2858^1476351022Hans Havermann08/2015
902524^36966-147751021Enzo Doria03/2013
9026(78557*2^169464+1)/16052751014Lelio R Paula06/2014
9027(34*10^51008-43)/951009Ray Chandler09/2010
902810^51004+12842751005Patrick De Geest08/2009
903010^51004-11351004Milton L. Brown12/2008
902910^51003+1695151004Patrick De Geest08/2009
903110^51003-7960151003Milton L. Brown12/2008
903210^51003-8083151003Milton L. Brown12/2008
903310^51002+887751003Patrick De Geest08/2009
903510^51002-1054151002Milton L. Brown11/2008
903410^51001+5205151002Patrick De Geest08/2009
903610^51001-15868751001Milton L. Brown10/2008
90372*10^51000+9351001Robert Price07/2016
9040(2^169416+5)/350999Lelio R Paula01/2012
9038(49*10^50998+41)/950999Robert Price07/2015
903913292^6867+6867^1329250999Hans Havermann02/2016
9041(35*10^50997-71)/950998Robert Price05/2015
90426^65536+2*97878-150997Jiahao He05/2017
904329^34871-28^3487150996Robert Price09/2012
904476^27112-7550993Norbert Schneider11/2012
9045(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
904610736^12645-12645^1073650971Norbert Schneider12/2016
9048(1017*2^169315-1)/971550968Lelio R Paula03/2015
90477^60309-6^(60309+1)50968Robert Price06/2016
90502^169267+9950955Lelio R Paula07/2009
90495*2^169264+350955Lelio R Paula02/2014
9051t(192517)50950Robert Price08/2014
905210^50943+62445150944Robert Price03/2015
905310^50943+5440950944Patrick De Geest02/2016
905410^50943-10055950943Patrick De Geest03/2016
90552^169206-364550937Lelio R Paula05/2009
90562^169196-11257750934Enzo Doria06/2014
905720^39146-348350931Enzo Doria03/2013
905810^50929+1684950930Patrick De Geest01/2012
906010^50929-5150929Robert Price05/2011
90597^60264+4850929Lelio R Paula10/2012
90612^169167+129950925Lelio R Paula05/2009
906210103^12717-10050925Enzo Doria07/2012
90633^106721-13050919Lelio R Paula07/2012
906518225^622+622^1822550917Anatoly F. Selevich11/2006
9064(10223*2^169138+1)/111350917Lelio R Paula05/2014
90667*2^169125+950913Lelio R Paula02/2014
9067(47*2^169123+1)/2950912Lelio R Paula03/2015
906820^39131+9350911Lelio R Paula01/2013
9069(21*27^35567-94921)/2650910Curtis Bright05/2015
9070(7*2^169124-1)/954950909Lelio R Paula01/2014
9071(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
907213693^5212+5212^1369350897Hans Havermann02/2016
90737*5^72813+650895Lelio R Paula09/2014
90745*10^50890-8150891Robert Price04/2017
90753^106656-1202850888Enzo Doria02/2013
9076(2^169028+3)/25950881Lelio R Paula01/2012
90772^169000-112750875Yves Minet05/2013
907819^39780+1650869Lelio R Paula01/2013
9079(19*2^168960+1)/550863Lelio R Paula07/2012
9080(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
908211^48840+4650862Lelio R Paula01/2013
9081(5*10^50861-107)/350862Robert Price01/2017
908320^39087-420350854Enzo Doria03/2013
9084(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
90852^168907-54444750847Paul Bourdelais11/2012
908619312^429+429^1931250839Anatoly F. Selevich12/2006
90875^72716-1322650827Enzo Doria02/2013
90882^168823+102550821Lelio R Paula01/2009
90897*10^50818-8950819Robert Price01/2017
90912^168811+15015*16881150818Henri Lifchitz02/2005
90902^168813-283350818Yves Minet09/2014
9092(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
90932^168795+538550813Lelio R Paula05/2009
90944*3^106483+550806Lelio R Paula03/2014
909513^45606+450803Lelio R Paula01/2013
909613^45606-3850803Lelio R Paula01/2013
90972^168746+5890550798Lelio R Paula05/2009
9098(16*10^50795-43)/950796Robert Price02/2015
9099gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
91007*10^50789-4750790Robert Price02/2017
91012^168717-72952350789Paul Bourdelais11/2012
9102(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9103(21*2^168652-1)/21550769Lelio R Paula01/2014
91042^168629+1290950763Lelio R Paula01/2011
91059328^12787+12787^932850762Norbert Schneider01/2016
91062^168627+7311350762Enzo Doria04/2016
91072^168623+4733350761Yves Minet02/2010
9108(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9109(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
91108544^12901-12901^854450723Norbert Schneider05/2017
9111(17^41221+1)/1850720Paul Bourdelais03/2010
911210^50711+750712Jason Earls12/2007
911310^50711-31796950711Patrick De Geest04/2009
9114(17^41213+3^41213)/2050710Robert Price08/2013
9115(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
91172^168431-15950703Lelio R Paula01/2011
9116(7*10^50702-1)/350703Erik Branger03/2014
9118117216#-p(117216)50700Henri Lifchitz03/2007
9119(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
9120(13*2^168352-1)/47750678Lelio R Paula01/2014
91218*10^50675+3950676Robert Price01/2017
9122(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
912314415^3274+3274^1441550670Hans Havermann05/2016
9124(12379^12379+282)/1750663Makoto Morimoto07/2016
91265^72480-1712650662Enzo Doria02/2013
9125(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
91273^106143+250644Mike Oakes11/2009
91289178^12777-12777^917850633Norbert Schneider02/2017
9129(2*10^50603-41)/350603Robert Price01/2017
9130(12^46889-1)/1150601Paul Bourdelais09/2008
91312^168068-189350594Yves Minet09/2012
91322^168057+841550591Lelio R Paula11/2011
91334*10^50579+950580Robert Price05/2015
91342^168019-9439550579Lelio R Paula07/2011
91352^168019+7421350579Enzo Doria04/2016
91363^106002+7050576Lelio R Paula07/2012
91375*2^167970-950565Lelio R Paula02/2014
9138(58*10^50558-13)/950559Robert Price09/2015
913988*10^50547+750549Robert Price11/2016
91402^167910-11262550546Enzo Doria06/2014
9141(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
91422^167866+1171550533Lelio R Paula05/2009
9143gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
91442^167847-13550527Lelio R Paula01/2011
9145-lucasV(-1,2,335684)50526Mike Oakes01/2017
9146(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
9147(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
91492^167807+7550515Lelio R Paula08/2010
91482^167805+7627750515Enzo Doria04/2016
91508335^12882+12882^833550510Norbert Schneider03/2016
91517*2^167777+950507Lelio R Paula02/2014
915214162^3681+3681^1416250502Hans Havermann05/2016
9153(17*10^50495-11)/350496Robert Price07/2015
91542^167682+8550478Lelio R Paula08/2010
91552^167667-92742750473Paul Bourdelais11/2012
91569737^12654+12654^973750470Norbert Schneider01/2016
9157(9179*2^167644-1)/1750469Lelio R Paula03/2015
915813386^5891+5891^1338650468Hans Havermann05/2016
9159(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
91605003^13637-15650447Enzo Doria07/2012
91616^64826-2672350445Enzo Doria03/2013
9162(3^105718+7)/3250439Lelio R Paula03/2012
9163(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
916417^40989+5650435Lelio R Paula01/2013
9165(12329^12329+1652)/42150435Makoto Morimoto07/2016
91662*5^72153+750434Lelio R Paula09/2014
9167(3126^14431-1)/312550433Richard Fischer03/2015
91688078^12907-12907^807850432Norbert Schneider05/2017
916939^31694+3850428Norbert Schneider05/2014
91702^167460+218750411Lelio R Paula11/2011
9171(12323^12323+2709)/2^450409Makoto Morimoto07/2016
917211^48400-771050404Enzo Doria02/2013
91732^167432+5461550403Lelio R Paula05/2009
9174(23*2^167430-1)/416950400Lelio R Paula01/2014
917568677!6-250395Robert Price07/2017
917619^39404+2250389Lelio R Paula01/2013
917735^32629-783450382Enzo Doria03/2013
91786^64744+16350381Lelio R Paula06/2012
9179116447#+17465950381Nicolas PALAU09/2016
91812^167353+12950379Lelio R Paula05/2009
918020^38722-113350379Enzo Doria03/2013
91833^105567-1650369Lelio R Paula07/2012
91822^167321-11284950369Enzo Doria06/2014
9184(28*10^50362-43)/350363Robert Price04/2016
918511421^12410-12410^1142150357Norbert Schneider08/2013
91862^167278-206350356Yves Minet03/2013
9187181^22300+22300^18150347Serge Batalov05/2014
91889932^12595-12595^993250343Norbert Schneider12/2016
91898993^12732-12732^899350342Norbert Schneider02/2017
91903*5^72018-450339Lelio R Paula09/2014
91912^167207-11268750335Enzo Doria06/2014
91926^64674-3750327Lelio R Paula06/2012
91932^167177+7480150326Enzo Doria04/2016
919413739^4600+4600^1373950323Hans Havermann10/2015
919511508^12391+12391^1150850320Norbert Schneider06/2014
91962^167132-216350312Yves Minet08/2013
91977^59527-6250307Lelio R Paula06/2012
9198(310027^9161+1)/31002850302Faysal YAtim04/2008
9199(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
92002^167083-11251950297Enzo Doria06/2014
9201272^20659-20659^27250296Norbert Schneider09/2015
920225337!!-1650290Robert Price06/2015
92039722^12611-12611^972250290Norbert Schneider12/2016
9204(15*2^167013+1)/64950275Lelio R Paula07/2012
920519^39315-1250275Lelio R Paula01/2013
92065^71925-3650274Lelio R Paula06/2012
92072^167002+279913950273Enzo Doria04/2016
920810957^12444-12444^1095750270Norbert Schneider07/2013
92098*10^50253-9950254Robert Price02/2017
92115^71894-5450252Lelio R Paula06/2012
9210(127^23887+1)/12850252Richard Fischer04/2017
921218^40028-550247Lelio R Paula01/2013
9213(3*2^166904+1)/127950241Lelio R Paula07/2012
921424^36397+2350236Norbert Schneider12/2013
92157984*29^34345+2150230Curtis Bright05/2015
92163^105248-1352850217Enzo Doria02/2013
92176^64532-6550216Lelio R Paula06/2012
92185^71834-2061650210Enzo Doria03/2013
9219(31*2^166778-1)/365150204Lelio R Paula01/2014
92202^166752-11239750198Enzo Doria06/2014
9221(12277^12277+1746)/17/37/15150197Makoto Morimoto07/2016
922311^48199-93050195Enzo Doria11/2012
92223*10^50194-750195Erik Branger11/2013
92249992^12549+12549^999250192Norbert Schneider10/2015
92252^166708+15750185Lelio R Paula01/2011
9226(1338272^8192+1)/6553750184Syoichiro Yamada06/2008
92277*2^166685+350179Lelio R Paula02/2014
92287*2^166671-950174Lelio R Paula02/2014
92299*2^166670+750174Lelio R Paula02/2014
92302^166670-11254150173Enzo Doria06/2014
92312^166657+46550169Lelio R Paula11/2011
923217^40768-2050163Lelio R Paula01/2013
92332^166596-7879550151Lelio R Paula07/2011
9234135^23541+13450151Norbert Schneider04/2015
923524^36335-67350150Enzo Doria03/2013
9236(12269^12269+291)/2^8/5/7/19/41/109/1042634950150Makoto Morimoto07/2016
9237(28*10^50147-97)/350148Robert Price07/2016
9238263^20718-20718^26350137Norbert Schneider09/2015
9239t(167020)50133Robert Price01/2015
9240(12263^12263+1442)/127/547950133Makoto Morimoto07/2016
92412868*(2340*(29023#-29527)*(2340*(29023#-29527)+3)+1)*(2868*(2340*(29023#-29527)*(2340*(29023#-29527)50129Pierre CAMI06/2008
924212^46445-1950123Lelio R Paula12/2012
92432^166501-1459350122Enzo Doria04/2013
9244(31*2^166509-1)/368407750120Lelio R Paula01/2014
92452^166483-16950117Lelio R Paula01/2011
92469^52515+2*6^52515-4^5251550113Mike Oakes04/2010
9247(23*2^166487-1)/3377049950112Lelio R Paula01/2014
92482*5^71689-950109Lelio R Paula09/2014
924913495^5154+5154^1349550096Hans Havermann04/2016
92506^64369-11950089Lelio R Paula06/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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